for an effective acceleration \(a\)  (whose expression can be inferred from [1]} using the dictionary described in the present work). More general forms of large-scale space-time dependence in the evolution equation can be introduced and dealt with using GHD [2]}. Another example is the exact expression for the diffusion operator, a second-derivative additional term in the kinetic equation. This is known in GHD [3]}, [4]}, and is conjectured to be applicable to large classes of integrable models, only requiring the knowledge of the scattering shift and the statistics. Thus, the results of the present work can directly be used to make a prediction for diffusion in the KdV soliton gas. A final example is the large-deviation function for fluctuations of soliton transport, which can be obtained from the theory developed in [5]}, [6]}.
